This Textbook of B.Sc. Mathematics is written for the students studying Second year First Semester in all universities of Telangana state was first published in the year 1988 and has undergone several editions and many reprints. The revised syllabus is being adopted by all universities in Andhra Pradesh, following Common Core Model Curriculum from the academic year 2015-2016(revised in 2016). The book strictly covers the new Curriculum for Semester III (2nd Year, 1st Semester).